If you are using Drupal 7 I would use Drupal Webform - together with the Webform CiviCRM integration module, since the Webform module let's you set the form to show within a block.
These are pure drupal webform settings. This is done under Adv Settings, which is on the Form settings tab ie at node/xx/webform/configure "Available as block:
If enabled this ...
Those are Smarty templates, and don't use regular CiviCRM tokens - which is confusing because the tokens can look the same.
Fortunately, Smarty is a full-fledged templating language. You can do date formatting pretty easily. I think you want this: